The talk was based on a joint paper with Sy-David Friedman and Liuzhen Wu with the same title. One of the most important areas of set theory is the descriptive set theory which lies on the border between general topology, classical logic, and recursion theory. Recently there have been applications of it also in functional analysis and other areas. One of new trends in the descriptive set theory is to generalize some of its beautiful results to the uncountable setting. The main result presented in this invited talk demonstrated one of the most striking differences between the countable (classical) and uncountable (new) branches of descriptive set theory. More precisely, in Gödel’s constructible universe L, for every successor cardinal we construct a GCH and cardinal preserving forcing poset P such that in the extension by P the ideal of all non-stationary subsets is Delta_1-definable. This means that the classical fact that all analytic co-analytic sets are Borel is not valid any longer for uncountable cardinals. This is a new application of the method of localization of R. David. After the talk there were many questions by such prominent set-theorists as R. Schindler, P. Welch, and others, which confirms that it was well-received.
B.04 Guest lecture
COBISS.SI-ID: 17435737The invited plenary talk was based on a joint paper with A. Bella and S. Tokgoz with the same title. In our talk we presented some of our new results, which came as a big surprise to several specialists from all around the world, taking part at the workshop, since they revealed several before unknown interconnections between classical combinatorial covering properties of remainders of topological groups and P-points. The latter have been intensively studied in recent decades. Following the talk there was a fruitful discussion with A. Arkhangelskii, the founder of this direction in the topological algebra. This confirms that the talk was well-received.
B.04 Guest lecture
COBISS.SI-ID: 17449817The talk was based on a joint paper with A. Bella and S. Tokgoz. This talk was devoted to the set-theoretic aspects of the same paper the talk in Messina (item 2 above) was devoted to. In particular, the fact that semifilters which coincide with their positive families and have the covering property of Menger can be used in the Silver forcing in the same way as non-meager P-filters, was quite a surprise for the audience.
B.04 Guest lecture